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LONDON, England (CNN) -- A British man charged with the murder of his American wife and baby near Boston will be extradited to the United States to face trial.

Neil Entwistle, 27, could be back in Massachusetts within the week, his lawyer Judith Seddon told reporters outside Bow Street Magistrates' Court in London.

Hours later, British Home Secretary Charles Clarke signed the extradition papers, a spokesman told CNN.

Seddon said her client would leave within the next week -- "at the earliest opportunity because he wants to cooperate with the authorities in any way that he can, and he is anxious that a delay may cause his late wife's family and his own additional distress, something he wishes to avoid.

"He believes that he will receive a fair and proper hearing in the USA of these very serious allegations."

Asked whether he denies the allegations, she said: "I'm sorry, I've got nothing further to add."

Entwistle was arrested Thursday at a London Underground station. At a court appearance a few hours later, he acknowledged the charges against him and said he did not consent to extradition.

But on Friday, his lawyers told the court that Entwistle would not fight extradition and wants to return to the United States "as soon as possible."

Seddon said her client had not changed his mind overnight but had only "reserved his position" on Thursday.

"He was always inclined to consent," she said.

In court Friday, the judge told Entwistle that his decision to voluntarily return would be irrevocable and asked if he understood what he was doing.

"Yes," Entwistle said.

He looked briefly at his father, Cliff Entwistle, as he signed a form consenting to return.

"I'm OK, Dad," Neil Entwistle told his father.

Entwistle faces two counts of murder, one count of illegal possession of a firearm and one count of illegal possession of ammunition, Massachusetts prosecutors said.

If convicted, he could face life in prison without parole. Massachusetts does not have the death penalty.

Entwistle's wife, Rachel, and their 9-month-old baby, Lillian, were found shot to death last month at their home in Hopkinton, Massachusetts, near Boston.

Middlesex County District Attorney Martha Coakley said authorities believe Rachel and Lillian Entwistle were killed sometime during the morning of January 20.

"There's no indication in the past of trouble," said Coakley, describing the picture investigators got of "a young couple starting out on a happy future."

A spokesman for Rachel Entwistle's family said members were "shocked by the news" of the charges against her husband.

"Rachel and Lily loved Neil very much. Neil was a trusted husband and father, and it is incomprehensible how that love and trust was betrayed in the ultimate act of violence," Joe Flaherty read from the family's statement.

There's not a clear-cut motive for the killings, but the investigation did turn up some "financial difficulty," Coakley said.

Entwistle had debts in England at the time he and his family left for the United States, Coakley said.

The investigation also found that Entwistle "may have found himself in financial difficulty" in the United Statesafter trying to start businesses "on the Internet, on eBay and also undertaking a lease and other financial obligations," Coakley said.

Authorities believe the killings were "possibly" intended to be a murder-suicide, "but we cannot confirm that," Coakley added.

"We know the defendant was aware" that Matterazzo owned guns, Coakley said, adding, "He had used that handgun with his father-in-law." Entwistle also had access to the gun, which was kept in a locked location, Coakley said.

Authorities say theybelieve Entwistle "secured" the gun before the killings and returned it to Matterazzo's home sometime during the late morning or afternoon of January 20,when no one was home, Coakley said.

"He was observed at Logan Airport" the next day, said Coakley. "He purchased a one-way ticket on British Airways at approximately 5 a.m. ... and was on an 8:15 flight to the United Kingdom that day."

Since his arrival in England, Entwistle had been staying at his parents' home in Worksop, about 150 miles north of London.

On January 22, the bodies of his wife and daughter were found in the rented home they had moved into just 10 days earlier. The next day police found Entwistle's car in a parking garage at Logan Airport.

No signs of struggle, prosecutor says

Rachel Entwistle, also 27, was shot in the head and died immediately, and her baby was shot in the stomach and bled to death within minutes, according to the medical examiner's report. It said that a small-caliber weapon was used but that an exact time of the deaths could not be determined.(Watch why it's tough to figure out when they died -- 1:34)

The bodies were found on the bed in the master bedroom covered with bedding. There were no signs of struggle, Coakley said. "It just looked like an unmade bed," she said, explaining why the first two searches failed to find the bodies.

Entwistle and his family had lived in the United States four to five months and began renting their home on January 12.

Rachel Entwistle's mother last spoke to her daughter on January 19. Friends showed up for dinner January 21 and found no one home, and Rachel's worried family called police.

Authorities did a cursory check in the home but found no one that day.

When the family filed a missing persons' report, a more thorough search was conducted January 22 and uncovered the bodies.

About 500 mourners attended their February 1 funeral service. Neil Entwistle did not return to the United States to attend. (Full story)

Last month, Entwistle refused, on the advice of his attorney, to answer questions by investigators who had traveled from Massachusetts to England.